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Information Security: Cryptography (part1). Dr. Shahriar Bijani Shahed University. Slides References. Matt Bishop, Computer Security: Art and Science , the author homepage, 2002-2004. Addam Schroll , Cryptography , Purdue university.

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### Information Security:Cryptography (part1)

Dr. ShahriarBijani

Shahed University

Slides References
• Matt Bishop, Computer Security: Art and Science, the author homepage, 2002-2004.
• AddamSchroll, Cryptography, Purdue university.
• Nikita Borisov, Cryptography, Illinois university, CS461, 2007.
Definitions
• Cryptography = the science of encryption
• Cryptanalysis = the science of breaking encryption
• Cryptology = cryptography + cryptanalysis
Definitions

Plaintext – A message in its natural format readable by an attacker

Ciphertext – Message altered to be unreadable by anyone except the intended recipients

Key – Sequence that controls the operation and behavior of the cryptographic algorithm

Keyspace– Total number of possible values of keys in a crypto algorithm

Definitions

Initialization Vector – Random values used with ciphers to ensure no patterns are created during encryption

Cryptosystem – The combination of algorithm, key, and key management functions used to perform cryptographic operations

Cryptosystem
• Quintuple (E, D, M, K, C)
• M set of plaintexts
• K set of keys
• C set of ciphertexts
• E set of encryption functions e: M KC
• D set of decryption functions d: C KM
Cryptosystem Services
• Confidentiality
• Integrity
• Authenticity
• Nonrepudiation
• Access Control
Types of Cryptography
• Stream-based Ciphers
• Mixes plaintext with key stream
• Good for real-time services
• Block Ciphers
• Substitution and transposition
Encryption Systems
• Substitution Cipher
• Convert one letter to another
• Cryptoquip
• Transposition Cipher
• Change position of letter in text
• Word Jumble
• Monoalphabetic Cipher
• E.g. Caesar
Encryption Systems
• Polyalphabetic Cipher
• E.g. Vigenère
• Modular Mathematics
• Running Key Cipher
• One-time Pads
• Randomly generated keys

10

Steganography
• Hiding a message within another medium, such as an image
• No key is required
• Example
• Modify color map of JPEG image
Cryptographic Methods
• Symmetric
• Known as Block Ciphers or Classical
• Same key for encryption and decryption
• Key distribution problem
• Asymmetric
• Mathematically related key pairs for encryption and decryption
• Public and private keys
Cryptographic Methods
• Hybrid
• Combines strengths of both methods
• Asymmetric distributes symmetric key
• Also known as a session key
• Symmetric provides bulk encryption
• Example:
• SSL negotiates a hybrid method
Symmetric Algorithms (Block Ciphers)
• DES / 3DES
• AES
• IDEA
• Blowfish
• RC4/ RC5
• CAST
• SAFER
• Twofish

Plaintext

E

Ciphertext

Key

D

Plaintext

Asymmetric Algorithms
• Diffie-Hellman
• RSA
• El Gamal
• Elliptic Curve Cryptography (ECC)
Hashing Algorithms
• MD5
• Computes 128-bit hash value
• Widely used for file integrity checking
• SHA-1
• Computes 160-bit hash value
• NIST approved message digest algorithm
Attacks
• Opponent whose goal is to break cryptosystem is the adversary
• Assume adversary knows algorithm used, but not key
• Three types of attacks:
• Ciphertext only: adversary has only ciphertext; goal is to find plaintext, possibly key
• Known plaintext: adversary has ciphertext, Learn (or guess) part of the corresponding plaintext, decrypt the rest plaintext; goal is to find key
• Chosen plaintext: adversary may supply plaintexts and obtain corresponding ciphertext; goal is to find key (or other messages)
Basis for Attacks
• Mathematical attacks
• Based on analysis of underlying mathematics
• Statistical attacks
• Make assumptions about the distribution of letters, pairs of letters (digrams), triplets of letters (trigrams), etc.
• Called models of the language
• Examine ciphertext, correlate properties with the assumptions.
Classical Cryptography
• Sender, receiver share common key
• Keys may be the same, or trivial to derive from one another
• Two basic types
• Transposition ciphers
• Substitution ciphers
• Combinations are called product ciphers
Transposition Cipher
• Rearrange letters in plaintext to produce ciphertext
• Example: Rail-Fence Cipher
• Plaintext is HELLO WORLD
• Rearrange as

HLOOL

ELWRD

• Ciphertext is HLOOL ELWRD
Attacking the Cipher
• Anagramming
• If 1-gram frequencies match English frequencies, but other n-gram frequencies do not, probably transposition
• Rearrange letters to form n-grams with highest frequencies
Example
• Ciphertext: HLOOLELWRD
• Frequencies of 2-grams beginning with H
• HE 0.0305
• HO 0.0043
• HL, HW, HR, HD < 0.0010
• Frequencies of 2-grams ending in H
• WH 0.0026
• EH, LH, OH, RH, DH ≤ 0.0002
• Implies E follows H
Example
• Arrange so the H and E are adjacent

HE

LL

OW

OR

LD

• Read off across, then down, to get original plaintext!
Substitution Ciphers
• Change characters in plaintext to produce ciphertext
• Example: Caesar cipher
• Plaintext is HELLO WORLD
• Change each letter to the third letter following it (X goes to A, Y to B, Z to C)
• Key is 3, usually written as letter ‘D’
• Ciphertext is KHOOR ZRUOG
• Each letter gets mapped to another letter
• E.g. A -> E, B -> R, C -> Q, ...
• What’s the key space?
• 26!
Caesar cipher
• Historical Ciphers

K=3

Outer: plaintext

Inner: ciphertext

Caesar cipher
• Formally
• Encrypt(Letter, Key) = (Letter + Key) (mod 26)
• Decrypt(Letter, Key) = (Letter - Key) (mod 26)
• Encrypt(“NIKITA”, 3) = “QLNLWD”
• Decrypt(“QLNLWD”, 3) = “NIKITA”
• More Formally
• M = { sequences of letters }
• K = { i | i is an integer and 0 ≤ i ≤ 25 }
• E = { Ek | kK and for all letters m,

Ek(m) = (m + k) mod 26 }

• D = { Dk | kK and for all letters c,

Dk(c) = (26 + c – k) mod 26 }

• C = M
Attacks
• Ciphertext only attack:
• Recover plaintext knowing only the ciphertext
• Ciphertext:
• HSPAA SLRUV DSLKN LPZHK HUNLY VBZAO PUN
Frequency analysis

HSPAA SLRUV DSLKN LPZHK HUNLY VBZAO PUN

• Find most frequent letters
• 4 times: L
• 3 times: A, H, N, P, S, U
• Guess: Decrypt(L) = E
• Key = L-E = 7
• Decrypt(HSPAA SLRUV DSLKN LPZHK HUNLY VBZAO PUN, 7) = ALITT LEKNO WLEDG EISAD ANGER OUSTH ING
Brute force
• Ciphertext = IGKYGXOYOTYKIAXK
• Decrypt(IGKYGXOYOTYKIAXK, 1) = HFJXFWNXNSXJHZWJ
• Decrypt(IGKYGXOYOTYKIAXK, 2) = GEIWEVMWMRWIGYVI
• Decrypt(IGKYGXOYOTYKIAXK, 3) = FDHVDULVLQVHFXUH
• Decrypt(IGKYGXOYOTYKIAXK, 4) = ECGUCTKUKPUGEWTG
• Decrypt(IGKYGXOYOTYKIAXK, 5) = DBFTBSJTJOTFDVSF
• Decrypt(IGKYGXOYOTYKIAXK, 6) = CAESARISINSECURE
Attacking the Cipher
• Exhaustive search
• If the key space is small enough, try all possible keys until you find the right one
• Caesar cipher has 26 possible keys
• Statistical analysis
• Compare to 1-gram model of English
Statistical Attack
• Compute frequency of each letter in ciphertext:

G 0.1 H 0.1 K 0.1 O 0.3

R 0.2 U 0.1 Z 0.1

• Apply 1-gram model of English
• Frequency of characters (1-grams) in English is on next slide
Statistical Analysis
• f(c) frequency of character c in ciphertext
• (i) correlation of frequency of letters in ciphertext with corresponding letters in English, assuming key is i
• (i) = 0 ≤ c ≤ 25f(c)p(c – i) so here,

(i) = 0.1p(6 – i) + 0.1p(7 – i) + 0.1p(10 – i) + 0.3p(14 – i) + 0.2p(17 – i) + 0.1p(20 – i) + 0.1p(25 – i)

• p(x) is frequency of character x in English
The Result
• Most probable keys, based on :
• i = 6, (i) = 0.0660
• plaintext EBIIL TLOLA
• i = 10, (i) = 0.0635
• plaintext AXEEH PHKEW
• i = 3, (i) = 0.0575
• plaintext HELLO WORLD
• i = 14, (i) = 0.0535
• plaintext WTAAD LDGAS
• Only English phrase is for i = 3
• That’s the key (3 or ‘D’)
Caesar’s Problem
• Key is too short
• Can be found by exhaustive search
• Statistical frequencies not concealed well
• They look too much like regular English letters
• So make it longer
• Multiple letters in key
• Idea is to smooth the statistical frequencies to make cryptanalysis harder